Time and Frequency Analysis of Particle Swarm Trajectories for Cognitive Machines

This paper examines the inherited persistent behavior of particle swarm optimization and its implications to cognitive machines. The performance of the algorithm is studied through an average particle’s trajectory through the parameter space of the Sphere and Rastrigin function. The trajectories are decomposed into position and velocity along each dimension optimized. A threshold is defined to separate the transient period, where the particle is moving towards a solution using information about the position of its best neighbors, from the steady state reached when the particles explore the local area surrounding the solution to the system. Using a combination of time and frequency domain techniques, the inherited long-term dependencies that drive the algorithm are discerned. Experimental results show the particles balance exploration of the parameter space with the correlated goal oriented trajectory driven by their social interactions. The information learned from this analysis can be used to extract complexity measures to classify the behavior and control of particle swarm optimization, and make proper decisions on what to do next. This novel analysis of a particle trajectory in the time and frequency domains presents clear advantages of particle swarm optimization and inherent properties that make this optimization algorithm a suitable choice for use in cognitive machines.